I am trying to solve the Non-linear Schrodinger equation
$-\Delta \psi(r) + \psi(r) - |\psi(r)|^2\psi(r) = 0$ where $r \in \Omega$
In a square domain ($(x,y) \in \Omega$ where $\Omega=[0,1]\times [0,1]$) with the Dirichlet condition
$\psi(r) = 0$ for $r \in \partial \Omega$
and with the additional constraint
$\int_\Omega d^2r \, |\psi(r)|^2 = 1$
Does somebody know how to include the integral condition into NDSolve?
Thanks in advance